English

Why random matrices share universal processes with interacting particle systems?

Mathematical Physics 2013-12-17 v2 Statistical Mechanics math.MP Probability

Abstract

In these lecture we explain why limiting distribution function, like the Tracy-Widom distribution, or limit processes, like the Airy_2 process, arise both in random matrices and interacting particle systems. The link is through a common mathematical structure on an interlacing structure, also known as Gelfand-Tsetlin pattern, that appears for specific models in both fields.

Keywords

Cite

@article{arxiv.1312.1126,
  title  = {Why random matrices share universal processes with interacting particle systems?},
  author = {Patrik L. Ferrari},
  journal= {arXiv preprint arXiv:1312.1126},
  year   = {2013}
}

Comments

Extended lecture notes of the ICTP minicourse in Trieste, September 2013. 45 pages, 6 figures; Minor corrections

R2 v1 2026-06-22T02:20:32.626Z